Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence
|
|
- Terence Stephens
- 5 years ago
- Views:
Transcription
1 Proceedngs of he weny-second Inernaonal Jon Conference on Arfcal Inellgence l, -Norm Regularzed Dscrmnave Feaure Selecon for Unsupervsed Learnng Y Yang, Heng ao Shen, Zhgang Ma, Z Huang, Xaofang Zhou School of Informaon echnology & Elecrcal Engneerng, he Unversy of Queensland. Deparmen of Informaon Engneerng & Compuer Scence, Unversy of reno. yangy zju@yahoo.com.cn, shenh@ee.uq.edu.au, ma@ds.unn., {huang, zxf}@ee.uq.edu.au. Absrac Compared wh supervsed learnng for feaure selecon, s much more dffcul o selec he dscrmnave feaures n unsupervsed learnng due o he lack of label nformaon. radonal unsupervsed feaure selecon algorhms usually selec he feaures whch bes preserve he daa dsrbuon, e.g., manfold srucure, of he whole feaure se. Under he assumpon ha he class label of npu daa can be predced by a lnear classfer, we ncorporae dscrmnave analyss and l, -norm mnmzaon no a jon framework for unsupervsed feaure selecon. Dfferen from exsng unsupervsed feaure selecon algorhms, our algorhm selecs he mos dscrmnave feaure subse from he whole feaure se n bach mode. Exensve expermen on dfferen daa ypes demonsraes he effecveness of our algorhm. Inroducon In many areas, such as compuer vson, paern recognon and bologcal sudy, daa are represened by hgh dmensonal feaure vecors. Feaure selecon ams o selec a subse of feaures from he hgh dmensonal feaure se for a compac and accurae daa represenaon. I has wofold role n mprovng he performance for daa analyss. Frs, he dmenson of seleced feaure subse s much lower, makng he subsequenal compuaon on he npu daa more effcen. Second, he nosy feaures are elmnaed for a beer daa represenaon, resulng n a more accurae cluserng and classfcaon resul. Durng recen years, feaure selecon has araced much research aenon. Several new feaure selecon algorhms have been proposed wh a varey of applcaons. Feaure selecon algorhms can be roughly classfed no wo groups,.e., supervsed feaure selecon and unsupervsed feaure selecon. Supervsed feaure selecon algorhms, e.g., Fsher score [Duda e al., ], robus regresson [Ne e al., ], sparse mul-oupu regresson [Zhao e al., ] and race rao [Ne e al., 8], usually selec feaures accordng o labels of he ranng daa. Because dscrmnave nformaon s enclosed n labels, supervsed feaure selecon s usually able o selec dscrmnave feaures. In unsupervsed scenaros, however, here s no label nformaon drecly avalable, makng much more dffcul o selec he dscrmnave feaures. A frequenly used creron n unsupervsed learnng s o selec he feaures whch bes preserve he daa smlary or manfold srucure derved from he whole feaure se [He e al., 5; Zhao and Lu, 7; Ca e al., ]. However, dscrmnave nformaon s negleced hough has been demonsraed mporan n daa analyss [Fukunaga, 99]. Mos of he radonal supervsed and unsupervsed feaure selecon algorhms evaluae he mporance of each feaure ndvdually [Duda e al., ; He e al., 5; Zhao and Lu, 7] and selec feaures one by one. A lmaon s ha he correlaon among feaures s negleced [Zhao e al., ; Ca e al., ]. More recenly, researchers have appled he wo-sep approach,.e., specral regresson, o supervsed and unsupervsed feaure selecon [Zhao e al., ; Ca e al., ]. hese effors have shown ha s a beer way o evaluae he mporance of he seleced feaures jonly. In hs paper, we propose a new unsupervsed feaure selecon algorhm by smulaneously explong dscrmnave nformaon and feaure correlaons. Because we ulze local dscrmnave nformaon, he manfold srucure s consdered oo. Whle [Zhao e al., ; Ca e al., ] also selec feaures n bach mode, our algorhm s a one-sep approach and s able o selec he dscrmnave feaures for unsupervsed learnng. We also propose an effcen algorhm o opmze he problem. he Objecve Funcon In hs secon, we gve he objecve funcon of he proposed Unsupervsed Dscrmnave Feaure Selecon (UDFS algorhm. Laer n he nex secon, we propose an effcen algorhm o opmze he objecve funcon. I s worh menonng ha UDFS ams o selec he mos dscrmnave feaures for daa represenaon, where manfold srucure s consdered, makng dfferen from he exsng unsupervsed feaure selecon algorhms. Denoe X = {x,x,..., x n } as he ranng se, where R d ( n s he -h daum and n s he oal x 589
2 number of ranng daa. In hs paper, I s deny marx. For a consan m, m R m s a column vecor wh all of s elemens beng and H m = I m m m R m m.foran arbrary marx A R r p, s l, -norm s defned as A, = r = p j= A j. ( Suppose he n ranng daa x,x,..., x n are sampled from c classes and here are n samples n he -h class. We defne y {, } c ( n as he label vecor of x. he j-h elemen of y s f x belongs o he j-h class, and oherwse. Y =[y,y,..., y n ] {, } n c s he label marx. he oal scaer marx S and beween class scaer marx S b are defned as follows [Fukunaga, 99]. n S = (x μ(x μ = X X ( = S b = c n (μ μ(μ μ = XGG X (3 = where μ s he mean of all samples, μ s he mean of samples n he -h class, n s he number of samples n he -h class, X = XH n s he daa marx afer beng cenered, and G = [G,..., G n ] = Y (Y Y / s he scaled label marx. A well-known mehod o ulze dscrmnave nformaon s o fnd a low dmensonal subspace n whch S b s maxmzed whle S s mnmzed [Fukunaga, 99]. Recenly, some researchers proposed wo dfferen new algorhms o explo local dscrmnave nformaon [Sugyama, 6; Yang e al., b] for classfcaon and mage cluserng, demonsrang ha local dscrmnave nformaon s more mporan han global one. Inspred by hs, for each daa pon x, we consruc a local se N k (x comprsng x and s k neares neghbors x,..., x k. Denoe X =[x,x,..., x k ] as he local daa marx. Smlar o ( and (3, he local oal scaer marx S ( and beween class scaer marx S ( b of N k (x are defned as follows. S ( = X X ; (4 S ( b = X G ( G X (, (5 where X = X H k+ and G ( =[G,G,..., G k ]. For he ease of represenaon, we defne he selecon marx S {, } n (k+ as follows. { f p = F {q}; (S pq = (6 oherwse, where F = {,,..., k }. In hs paper, remans unclear how o defne G because we are focusng on unsupervsed learnng where here s no label nformaon avalable. In order o make use of local dscrmnave nformaon, we assume here s a lnear classfer W R d c whch classfes each daa pon o a class,.e., G = W x. Noe ha G,G,..., G k are seleced from G,.e., G ( = S G.hen we have G ( =[G,G,..., G k ] = S G = S X W. (7 I s worh nong ha he proposed algorhm s an unsupervsed one. In oher words, G defned n (7 s he oupu of he algorhm,.e., G = W x, bu no provded by he human supervsors. If some rows of W shrnk o zero, W can be regarded as he combnaon coeffcens for dfferen feaures ha bes predc he class labels of he ranng daa. Nex, we gve he approach whch learns a dscrmnave W for feaure selecon. Inspred by [Fukunaga, 99; Yang e al., b], we defne he local dscrmnave score DS of x as [ ] DS = r (S ( + λi S ( b = r [G X ] ( ( X X + λi XG ( (8 [ ] = r W XS X ( X X + λi XS X W, where λ s a parameer and λi s added o make he erm ( X X + λi nverble. Clearly, a larger DS ndcaes ha W has a hgher dscrmnave ably w.r.. he daum x.we nend o ran a W correspondng o he hghes dscrmnave scores for all he ranng daa x,..., x n. herefore we propose o mnmze (9 for feaure selecon. n } {r[g ( H k+g ( ] DS + W, (9 = Consderng ha he daa number n each local se s usually small, G ( H k+g ( s added n (9 o avod overfng. he regularzaon erm W, conrols he capacy of W and also ensures ha W s sparse n rows, makng parcularly suable for feaure selecon. Subsung DS n (9 by (8, he objecve funcon of our UDSF s gven by n mn r{w XS H k+ S W X W W =I = ( [W XS X ( X X + λi XS X W ]} + W, where he orhogonal consran s mposed o avod arbrary scalng and avod he rval soluon of all zeros. Noe ha he frs erm of ( s equvalen o he followng : n r{w X{ [S (H k+ X ( X X + λi X S ]}X W } = Meanwhle we have H k+ X ( X X + λi X =H k+ H k+ X ( X X + λi XH k+ =H k+ H k+ ( X X + λi ( X X + λi X ( X X + λi XH k+ =H k+ H k+ ( X X + λi X XH k+ =H k+ H k+ ( X X + λi ( X X + λi λih k+ =λh k+ ( X X + λi H k+ herefore, he objecve funcon of UDFS s rewren as mn r(w MW+ W, ( W W =I I can be also nerpreed n regresson vew [Yang e al., a]. 59
3 where M = X [ n = ( S H k+ ( X X + λi H k+ S ] X ( Denoe w as he -h row of W,.e., W =[w,...w d ],he objecve funcon shown n ( can be also wren as mn r(w MW+ d w. (3 W W =I = We can see ha many rows of he opmal W correspondng o (3 shrnk o zeros. Consequenly, for a daum x, x = W x s a new represenaon of x usng only a small se of seleced feaures. Alernavely, we can rank each feaure f d = accordng o w n descendng order and selec op ranked feaures. Opmzaon of UDFS Algorhm he l, -norm mnmzaon problem has been suded n several prevous works, such as [Argyrou e al., 8; Ne e al., ; Oboznsk e al., 8; Lu e al., 9; Zhao e al., ; Yang e al., ]. However, remans unclear how o drecly apply he exsng algorhms o opmzng our objecve funcon, where he orhogonal consran W W = I s mposed. In hs secon, nspred by [Ne e al., ], we gve a new approach o solve he opmzaon problem shown n ( for feaure selecon. We frs descrbe he dealed approach of UDFS algorhm n Algorhm as follows. Algorhm : he UDFS algorhm. for =o n do B =( X X + λi 3 M = S H k+ B H k+ S ( ; n 4 M = X M X ; = 5 Se =and nalze D R d d as an deny marx; 6 repea 7 P = M + D ; 8 W =[p,..., p c ] where p,..., p c are he egenvecors of P correspondng o he frs c smalles egenvalues; 9 Updae he dagonal marx D + as D + = w... w d ; = +; unl Convergence; Sor each feaure f d = accordng o w n descendng order and selec he op ranked ones. Below, we brefly analyze Algorhm- proposed n hs secon. From lne o lne 4, compues M defned n Usually, many rows of he opmal W are close o zeros. (. From lne 6 o lne, opmzes he objecve funcon shown n (3. Nex, we verfy ha he proposed erave approach,.e., lne 6 o lne n Algorhm, converges o he opmal W correspondng o (3. We begn wh he followng wo Lemmas. Lemma. For any wo non-zero consans a and b, he followng nequaly holds [Ne e al., ]. a a b b b b. (4 P roof. he dealed proof s smlar as ha n [Ne e al., ]. Lemma. he followng nequaly holds provded ha v r = are non-zero vecors, where r s an arbrary number [Ne e al., ]. v+ v + v v (5 v v P roof. Subsung a and b n (4 by v + and v respecvely, we can see ha he followng nequaly holds for any. v v + + v v v (6 v Summng (6 over, can be seen ha (5 holds. Nex, we show ha he erave algorhm shown n Algorhm- converges by he followng heorem. heorem. he erave approach n Algorhm (lne 6 o lne monooncally decreases he objecve funcon value of mn r(w MW+ d W = w W =I n each eraon 3. P roof. Accordng o he defnon of W n lne 8 of Algorhm, we can see ha herefore, we have W = arg mn r[w (M + D W ] (7 W W =I r[w (M + D W ] r[w (M + D W ] r(w MW + w w r(wmw + w w 3 When compung D +, s dagonal elemen d =. w I s worhy nong ha n pracce, w could be very close o zero bu no zero. However, w can be zero heorecally. In hs case, we can follow he radonal regularzaon way and defne d =,whereς s a very small consan. When ς w +ς s easy o see ha w approxmaes. +ς w 59
4 hen we have he followng nequaly r(w MW + w ( r(w MW + ( w w w Meanwhle, accordng o Lemma, w w w we have he followng nequaly: r(w + AW ++ w + w w. r(w AW + w w w w w herefore, w, whch ndcaes ha he objecve funcon value of mn r(w MW+ d W = w W =I monooncally decreases usng he updang rule n Algorhm. Accordng o heorem, we can see ha he erave approach n Algorhm converges o he opmal W correspondngo (3. Because k s much smaller han n, he me complexy of compung M defned n ( s abou O(n. o opmze he objecve funcon of UDFS, he mos me consumng operaon s o perform egen-decomposon of P. Noe ha P R d d. he me complexy of hs operaon s O(d 3 approxmaely. Expermens In hs secon, we es he performance of UDFS proposed n hs paper. Followng [He e al., 5; Ca e al., ], we es he performance of he proposed algorhm n erms of cluserng. Expermen Seup In our expermen, we have colleced a dversy of 6 publc daases o compare he performance of dfferen unsupervsed feaure selecon algorhms. hese daases nclude hree face mage daases,.e., UMIS 4, FERE 5 and YALEB [Georghades e al., ], one ga mage daase,.e., USF HumanID [Sarkar e al., 5], one spoken leer recognon daa,.e., Isole 6 and one hand wren dg mage daase,.e., USPS [Hull, 994]. Dealed nformaon of he sx daases s summarzed n able. We compare UDFS proposed n hs paper wh he followng unsupervsed feaure selecon algorhms. 4 hp://mages.ee.ums.ac.uk/danny/daabase.hml 5 hp:// 6 hp:// mlearn/mlsummary.hml able : Daabase Descrpon. Daase Sze # of Feaures # of Classes UMIS FERE 4 96 YALEB USF HumanID Isole USPS All Feaures whch adops all he feaures for cluserng. I s used as he baselne mehod n hs paper. Max Varance whch selecs he feaures correspondng o he maxmum varances. Laplacan Score [He e al., 5] whch selecs he feaures mos conssen wh he Gaussan Laplacan marx. Feaure Rankng [Zhao and Lu, 7] whch selecs feaures usng specral regresson. Mul-Cluser Feaure Selecon (MCFS [Ca e al., ] whch selecs feaures usng specral regresson wh l -norm regularzaon. For LS, MCFS and UDFS, we fx k, whch specfes he sze of neghborhood, a 5 for all he daases. For LS and FR, we need o une he bandwdh parameer for Gaussan kernel, and for MCFS and UDFS we need o une he regularzaon parameer. o farly compare dfferen unsupervsed feaure selecon algorhms, we une hese parameers from { 9, 6, 3,, 3, 6, 9 }. We se he number of seleced feaures as {5,, 5,, 5, 3} for he frs fve daases. Because he oal feaure number of USPS s 56, we se he number of seleced feaures as {5, 8,, 4, 7, } for hs daase. We repor he bes resuls of all he algorhms usng dfferen parameers. In our expermen, each feaure selecon algorhm s frs performed o selec feaures. hen K-means cluserng algorhm s performed based on he seleced feaures. Because he resuls of K-means cluserng depend on nalzaon, s repeaed mes wh random nalzaons. We repor he average resuls wh sandard devaon (sd. wo evaluaon mercs,.e., Accuracy (ACC and Normalzed Muual Informaon (NMI, are used as evaluaon mercs n hs paper. Denoe q as he cluserng resuls and p as he ground ruh label of x. ACC s defned as follows. n = ACC = δ(p,map(q (8 n where δ(x, y = f x = y; δ(x, y = oherwse, and map(q s he bes mappng funcon ha permues cluserng labels o mach he ground ruh labels usng he Kuhn- Munkres algorhm. A larger ACC ndcaes beer performance. Gven wo varables P and Q, NMI s defned n (9. I(P, Q NMI(P, Q =, (9 H(P H(Q where I(P, Q s he muual nformaon beween P and Q, and H(P and H(Q are he enropes of P and Q [Srehl and 59
5 able : Cluserng Resuls (ACC% ± sd of Dfferen Feaure Selecon Algorhms All Feaures Max Varance Laplacan Score Feaure Rankng MCFS UDFS UMIS 4.9 ± ± ± ± ± ± 3.8 FERE. ±.5. ±.3.4 ±.5.8 ±.5 5. ±.7 6. ±.6 YALEB. ± ±.3.4 ± ±.8.4 ±. 4.7 ±.6 USF HumanID 3. ±.6.9 ± ±.3. ±. 3. ± ±.8 Isole 57.8 ± ± ± ±.9 6. ± ± 3.6 USPS 6.9 ± ± ± ± ± ± 3.3 able 3: Cluserng Resuls (NMI% ± sd of Dfferen Feaure Selecon Algorhms All Feaures Max Varance Laplacan Score Feaure Rankng MCFS UDFS UMIS 6.9 ± ± ± ± ± ±. FERE 6.7 ± ± ± ± ± ±.4 YALEB 4. ±.7 3. ± ±..3 ± ±. 5.4 ±.9 USF HumanID 5.9 ± ± ±. 9.3 ± ± ±.5 Isole 74. ± ±. 7. ±. 7.5 ± ± ±.3 USPS 59. ± ±. 6. ± ±. 6. ± ±.5 Ghosh, ]. Denoe l as he number of daa n he cluser C l ( l c accordng o cluserng resuls and h be he number of daa n he h-h ground ruh class ( h c. NMIsdefnedasfollows[Srehl and Ghosh, ]: c c l= h= NMI = l,h log( n l,h l h (c l= l log ( l c, ( n h= h log hn where l,h s he number of samples ha are n he nersecon beween he cluser C l and he h-h ground ruh class. Agan, a larger NMI ndcaes a beer cluserng resul. Expermenal Resuls and Dscusson Frs, we compare he performance of dfferen feaure selecon algorhms. he expermen resuls are shown n able and able 3. We can see from he wo ables ha he cluserng resuls of All Feaures are beer han hose of Max Varance. However, because he feaure number s sgnfcanly reduced by performng Max Varance for feaure selecon, resulng n he subsequenal operaon, e.g., cluserng, faser. herefore, s more effcen. he resuls from oher feaure selecon algorhms are generally beer han All Feaures and also more effcen. Excep for Max Varance, all of he oher feaure selecon algorhms are non-lnear approaches. We conclude ha local srucure s crucal for feaure selecon n many applcaons, whch s conssen wh prevous work on feaure selecon [He e al., 5]. We can also see from he wo ables ha MCFS gans he second bes performance. Boh Feaure Rankng [Zhao and Lu, 7] and MCFS [Ca e al., ] adop a wo-sep approach,.e, specral regresson, for feaure selecon. he dfference s ha Feaure Rankng analyzes feaures separaely and selecs feaures one afer anoher bu MCFS selecs feaures n bachmode. hs observaon valdaes ha s a beer way o analyze daa feaures jonly for feaure selecon. Fnally, we observe ha he UDFS algorhm proposed n hs paper obans he bes performance. here are wo man reasons for hs. Frs, UDFS analyzes feaures jonly. Second, UDFS smulaneously ulzes dscrmnave nformaon and local srucure of daa dsrbuon. Nex, we sudy he performance varaon of UDFS wh respec o he regularzaon parameer n ( and he number of seleced feaures. Due o he space lm, we use he hree face mage daases as examples. he expermenal resuls are shown n Fg.. We can see from Fg. ha he performance s no very sensve o as long as s smaller han. However, he performance s comparavely sensve o he number of seleced feaures. How o decde he number of seleced feaures s daa dependen and sll an open problem. Concluson Whle has been shown n many prevous works ha dscrmnave nformaon s benefcal o many applcaons, s no ha sraghforward o ulze n unsupervsed learnng due o he lack of label nformaon. In hs paper, we have proposed a new unsupervsed feaure selecon algorhm whch s able o selec dscrmnave feaures n bach mode. An effcen algorhm s proposed o opmze he l, -norm regularzed mnmzaon problem wh orhogonal consran. Dfferen from exsng algorhms whch selec he feaures whch bes preserve daa srucure of he whole feaure se, UDFS proposed n hs paper s able o selec dscrmnave feaure for unsupervsed learnng. We show ha s a beer way o selec dscrmnave feaures for daa represenaon and UDFS ouperforms he exsng unsupervsed feaure selecon algorhms. Acknowledgemen hs work s suppored by ARC DP94678 and parally suppored by he FP7-IP GLOCAL european projec. 593
6 ACC.4 ACC. ACC....5 ^ 9 ^ 6 ^ 3 ^3 ^6 ^ ^ 9 ^ 6 ^ 3 ^3 ^6 ^ ^ 9 ^ 6 ^ 3 ^3 ^6 ^ (a UMIS-ACC (b FERE-ACC (c YALEB-ACC NMI.4 NMI.4 NMI.... ^ 9 ^ 6 ^ 3 ^3 ^6 ^ ^ 9 ^ 6 ^ 3 ^3 ^6 ^ ^ 9 ^ 6 ^ 3 ^3 ^6 ^ (d UMIS-NMI (e FERE-NMI (f YALEB-NMI Fgure : Performance varaon of UDFS w.r. dfferen parameers. References [Oboznsk e al., 8] G. Oboznsk, M. J. Wanwrgh, [Argyrou e al., 8] Andreas Argyrou, heodoros Evgenou, Massmlano Ponl, Andreas Argyrou, heodoros n mulvarae regresson. In NIPS, 8. and M. I. Jordan. Hghdmensonal unon suppor recovery Evgenou, and Massmlano Ponl. Convex mul-ask [Sarkar e al., 5] S. Sarkar, P.J. Phllps, Z. Lu, I.R. Vega, feaure learnng. In Machne Learnng, 8. P. Groher, and K.W. Bowyer. he humand ga challenge problem: daa ses, performance, and analyss. IEEE [Ca e al., ] Deng Ca, Chyuan Zhang, and Xaofe He. Unsupervsed feaure selecon for mul-cluser daa. PAMI, pages 7(:6 77, 5. KDD,. [Srehl and Ghosh, ] A. Srehl and J. Ghosh. Cluser [Duda e al., ] R.O. Duda, P.E. Har, and D.G. Sork. ensembles a knowledge reuse framework for combnng Paern Classfcaon (nd Edon. John Wley & Sons, mulple parons. Journal of Machne Learnng Research, 3:583 67,. New York, USA,. [Fukunaga, 99] K. Fukunaga. Inroducon o sascal [Sugyama, 6] Masash Sugyama. Local fsher dscrmnan analyss for supervsed dmensonaly reducon. In paern recognon (nd Edon. Academc Press Professonal, Inc, San Dego, USA, 99. ICML, 6. [Georghades e al., ] A. Georghades, P. Belhumeur, [Yang e al., a] Y Yang, Fepng Ne, Shmng Xang, and D. Kregman. From few o many: Illumnaon cone Yueng Zhuang, and Wenhua Wang. Local and global models for face recognon under varable lghng and regressve mappng for manfold learnng wh ou-ofsample exrapolaon. In AAAI,. pose. IEEE PAMI, page 3(6:64366,. [He e al., 5] Xaofe He, Deng Ca, and Parha Nyog. [Yang e al., b] Y Yang, Dong Xu, Fepng Ne, Laplacan score for feaure selecon. NIPS, 5. Shucheng Yan, and Yueng Zhuang. Image cluserng usng local dscrmnan models and global negraon. IEEE [Hull, 994] J.J. Hull. A daabase for handwren ex recognon research. IEEE ransacons on Paern Analyss IP, pages 9(76 773,. and Machne Inellgence, pages 6(5:55 554, 994. [Yang e al., ] Yang Yang, Y Yang, Z Huang, Heng ao Shen, and Fepng Ne. ag localzaon wh [Lu e al., 9] Jun Lu, Shuwang J, and Jepng Ye. spaal correlaons and jon group sparsy. In CVPR, Mul-ask feaure learnng va effcen l, -norm mnmzaon. In UAI, 9. pages ,. [Zhao and Lu, 7] Zheng Zhao and Huan Lu. Specral [Ne e al., 8] Fepng Ne, Shmng Xang, Yangqng Ja, feaure selecon for supervsed and unsupervsed learnng. Changshu Zhang, and Shucheng Yan. race rao creron for feaure selecon. In AAAI, 8. In ICML, 7. [Zhao e al., ] Z. Zhao, L. Wang, and H. Lu. Effcen [Ne e al., ] Fepng Ne, Heng Huang, Xao Ca, and specral feaure selecon wh mnmum redundancy. In Chrs Dng. Effcen and robus feaure selecon va jon AAAI,. l, -norms mnmzaon. In NIPS,. 594
Robust and Accurate Cancer Classification with Gene Expression Profiling
Robus and Accurae Cancer Classfcaon wh Gene Expresson Proflng (Compuaonal ysems Bology, 2005) Auhor: Hafeng L, Keshu Zhang, ao Jang Oulne Background LDA (lnear dscrmnan analyss) and small sample sze problem
More informationAn introduction to Support Vector Machine
An nroducon o Suppor Vecor Machne 報告者 : 黃立德 References: Smon Haykn, "Neural Neworks: a comprehensve foundaon, second edon, 999, Chaper 2,6 Nello Chrsann, John Shawe-Tayer, An Inroducon o Suppor Vecor Machnes,
More informationAdvanced Machine Learning & Perception
Advanced Machne Learnng & Percepon Insrucor: Tony Jebara SVM Feaure & Kernel Selecon SVM Eensons Feaure Selecon (Flerng and Wrappng) SVM Feaure Selecon SVM Kernel Selecon SVM Eensons Classfcaon Feaure/Kernel
More informationCS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 4
CS434a/54a: Paern Recognon Prof. Olga Veksler Lecure 4 Oulne Normal Random Varable Properes Dscrmnan funcons Why Normal Random Varables? Analycally racable Works well when observaon comes form a corruped
More informationClustering (Bishop ch 9)
Cluserng (Bshop ch 9) Reference: Daa Mnng by Margare Dunham (a slde source) 1 Cluserng Cluserng s unsupervsed learnng, here are no class labels Wan o fnd groups of smlar nsances Ofen use a dsance measure
More informationOnline Supplement for Dynamic Multi-Technology. Production-Inventory Problem with Emissions Trading
Onlne Supplemen for Dynamc Mul-Technology Producon-Invenory Problem wh Emssons Tradng by We Zhang Zhongsheng Hua Yu Xa and Baofeng Huo Proof of Lemma For any ( qr ) Θ s easy o verfy ha he lnear programmng
More informationMachine Learning Linear Regression
Machne Learnng Lnear Regresson Lesson 3 Lnear Regresson Bascs of Regresson Leas Squares esmaon Polynomal Regresson Bass funcons Regresson model Regularzed Regresson Sascal Regresson Mamum Lkelhood (ML)
More informationMachine Learning 2nd Edition
INTRODUCTION TO Lecure Sldes for Machne Learnng nd Edon ETHEM ALPAYDIN, modfed by Leonardo Bobadlla and some pars from hp://www.cs.au.ac.l/~aparzn/machnelearnng/ The MIT Press, 00 alpaydn@boun.edu.r hp://www.cmpe.boun.edu.r/~ehem/mle
More informationDynamic Team Decision Theory. EECS 558 Project Shrutivandana Sharma and David Shuman December 10, 2005
Dynamc Team Decson Theory EECS 558 Proec Shruvandana Sharma and Davd Shuman December 0, 005 Oulne Inroducon o Team Decson Theory Decomposon of he Dynamc Team Decson Problem Equvalence of Sac and Dynamc
More informationVariants of Pegasos. December 11, 2009
Inroducon Varans of Pegasos SooWoong Ryu bshboy@sanford.edu December, 009 Youngsoo Cho yc344@sanford.edu Developng a new SVM algorhm s ongong research opc. Among many exng SVM algorhms, we wll focus on
More informationBayes rule for a classification problem INF Discriminant functions for the normal density. Euclidean distance. Mahalanobis distance
INF 43 3.. Repeon Anne Solberg (anne@f.uo.no Bayes rule for a classfcaon problem Suppose we have J, =,...J classes. s he class label for a pxel, and x s he observed feaure vecor. We can use Bayes rule
More informationRobustness Experiments with Two Variance Components
Naonal Insue of Sandards and Technology (NIST) Informaon Technology Laboraory (ITL) Sascal Engneerng Dvson (SED) Robusness Expermens wh Two Varance Componens by Ana Ivelsse Avlés avles@ns.gov Conference
More informationIntroduction to Boosting
Inroducon o Boosng Cynha Rudn PACM, Prnceon Unversy Advsors Ingrd Daubeches and Rober Schapre Say you have a daabase of news arcles, +, +, -, -, +, +, -, -, +, +, -, -, +, +, -, + where arcles are labeled
More informationLecture 6: Learning for Control (Generalised Linear Regression)
Lecure 6: Learnng for Conrol (Generalsed Lnear Regresson) Conens: Lnear Mehods for Regresson Leas Squares, Gauss Markov heorem Recursve Leas Squares Lecure 6: RLSC - Prof. Sehu Vjayakumar Lnear Regresson
More informationJohn Geweke a and Gianni Amisano b a Departments of Economics and Statistics, University of Iowa, USA b European Central Bank, Frankfurt, Germany
Herarchcal Markov Normal Mxure models wh Applcaons o Fnancal Asse Reurns Appendx: Proofs of Theorems and Condonal Poseror Dsrbuons John Geweke a and Gann Amsano b a Deparmens of Economcs and Sascs, Unversy
More informationSingle-loop System Reliability-Based Design & Topology Optimization (SRBDO/SRBTO): A Matrix-based System Reliability (MSR) Method
10 h US Naonal Congress on Compuaonal Mechancs Columbus, Oho 16-19, 2009 Sngle-loop Sysem Relably-Based Desgn & Topology Opmzaon (SRBDO/SRBTO): A Marx-based Sysem Relably (MSR) Mehod Tam Nguyen, Junho
More informationCHAPTER 10: LINEAR DISCRIMINATION
CHAPER : LINEAR DISCRIMINAION Dscrmnan-based Classfcaon 3 In classfcaon h K classes (C,C,, C k ) We defned dscrmnan funcon g j (), j=,,,k hen gven an es eample, e chose (predced) s class label as C f g
More informationOutline. Probabilistic Model Learning. Probabilistic Model Learning. Probabilistic Model for Time-series Data: Hidden Markov Model
Probablsc Model for Tme-seres Daa: Hdden Markov Model Hrosh Mamsuka Bonformacs Cener Kyoo Unversy Oulne Three Problems for probablsc models n machne learnng. Compung lkelhood 2. Learnng 3. Parsng (predcon
More informationCS 536: Machine Learning. Nonparametric Density Estimation Unsupervised Learning - Clustering
CS 536: Machne Learnng Nonparamerc Densy Esmaon Unsupervsed Learnng - Cluserng Fall 2005 Ahmed Elgammal Dep of Compuer Scence Rugers Unversy CS 536 Densy Esmaon - Cluserng - 1 Oulnes Densy esmaon Nonparamerc
More informationLecture VI Regression
Lecure VI Regresson (Lnear Mehods for Regresson) Conens: Lnear Mehods for Regresson Leas Squares, Gauss Markov heorem Recursve Leas Squares Lecure VI: MLSC - Dr. Sehu Vjayakumar Lnear Regresson Model M
More informationSolution in semi infinite diffusion couples (error function analysis)
Soluon n sem nfne dffuson couples (error funcon analyss) Le us consder now he sem nfne dffuson couple of wo blocks wh concenraon of and I means ha, n a A- bnary sysem, s bondng beween wo blocks made of
More informationLecture 11 SVM cont
Lecure SVM con. 0 008 Wha we have done so far We have esalshed ha we wan o fnd a lnear decson oundary whose margn s he larges We know how o measure he margn of a lnear decson oundary Tha s: he mnmum geomerc
More informationRobust Principal Component Analysis with Non-Greedy l 1 -Norm Maximization
Proceedngs of he Tweny-Second Inernaonal Jon Conference on Arfcal Inellgence Robus Prncpal Componen Analyss wh Non-Greedy l -Norm Maxmzaon Fepng Ne, Heng Huang, Chrs Dng, Djun Luo, Hua Wang Deparmen of
More information( ) [ ] MAP Decision Rule
Announcemens Bayes Decson Theory wh Normal Dsrbuons HW0 due oday HW o be assgned soon Proec descrpon posed Bomercs CSE 90 Lecure 4 CSE90, Sprng 04 CSE90, Sprng 04 Key Probables 4 ω class label X feaure
More informationFACIAL IMAGE FEATURE EXTRACTION USING SUPPORT VECTOR MACHINES
FACIAL IMAGE FEATURE EXTRACTION USING SUPPORT VECTOR MACHINES H. Abrsham Moghaddam K. N. Toos Unversy of Technology, P.O. Box 635-355, Tehran, Iran moghadam@saba.knu.ac.r M. Ghayoum Islamc Azad Unversy,
More informationDetection of Waving Hands from Images Using Time Series of Intensity Values
Deecon of Wavng Hands from Images Usng Tme eres of Inensy Values Koa IRIE, Kazunor UMEDA Chuo Unversy, Tokyo, Japan re@sensor.mech.chuo-u.ac.jp, umeda@mech.chuo-u.ac.jp Absrac Ths paper proposes a mehod
More informationCubic Bezier Homotopy Function for Solving Exponential Equations
Penerb Journal of Advanced Research n Compung and Applcaons ISSN (onlne: 46-97 Vol. 4, No.. Pages -8, 6 omoopy Funcon for Solvng Eponenal Equaons S. S. Raml *,,. Mohamad Nor,a, N. S. Saharzan,b and M.
More information( t) Outline of program: BGC1: Survival and event history analysis Oslo, March-May Recapitulation. The additive regression model
BGC1: Survval and even hsory analyss Oslo, March-May 212 Monday May 7h and Tuesday May 8h The addve regresson model Ørnulf Borgan Deparmen of Mahemacs Unversy of Oslo Oulne of program: Recapulaon Counng
More informationComputing Relevance, Similarity: The Vector Space Model
Compung Relevance, Smlary: The Vecor Space Model Based on Larson and Hears s sldes a UC-Bereley hp://.sms.bereley.edu/courses/s0/f00/ aabase Managemen Sysems, R. Ramarshnan ocumen Vecors v ocumens are
More informationAttribute Reduction Algorithm Based on Discernibility Matrix with Algebraic Method GAO Jing1,a, Ma Hui1, Han Zhidong2,b
Inernaonal Indusral Informacs and Compuer Engneerng Conference (IIICEC 05) Arbue educon Algorhm Based on Dscernbly Marx wh Algebrac Mehod GAO Jng,a, Ma Hu, Han Zhdong,b Informaon School, Capal Unversy
More informationMath 128b Project. Jude Yuen
Mah 8b Proec Jude Yuen . Inroducon Le { Z } be a sequence of observed ndependen vecor varables. If he elemens of Z have a on normal dsrbuon hen { Z } has a mean vecor Z and a varancecovarance marx z. Geomercally
More informationOn One Analytic Method of. Constructing Program Controls
Appled Mahemacal Scences, Vol. 9, 05, no. 8, 409-407 HIKARI Ld, www.m-hkar.com hp://dx.do.org/0.988/ams.05.54349 On One Analyc Mehod of Consrucng Program Conrols A. N. Kvko, S. V. Chsyakov and Yu. E. Balyna
More informationAnomaly Detection. Lecture Notes for Chapter 9. Introduction to Data Mining, 2 nd Edition by Tan, Steinbach, Karpatne, Kumar
Anomaly eecon Lecure Noes for Chaper 9 Inroducon o aa Mnng, 2 nd Edon by Tan, Senbach, Karpane, Kumar 2/14/18 Inroducon o aa Mnng, 2nd Edon 1 Anomaly/Ouler eecon Wha are anomales/oulers? The se of daa
More informationNew M-Estimator Objective Function. in Simultaneous Equations Model. (A Comparative Study)
Inernaonal Mahemacal Forum, Vol. 8, 3, no., 7 - HIKARI Ld, www.m-hkar.com hp://dx.do.org/.988/mf.3.3488 New M-Esmaor Objecve Funcon n Smulaneous Equaons Model (A Comparave Sudy) Ahmed H. Youssef Professor
More information[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5
TPG460 Reservor Smulaon 08 page of 5 DISCRETIZATIO OF THE FOW EQUATIOS As we already have seen, fne dfference appromaons of he paral dervaves appearng n he flow equaons may be obaned from Taylor seres
More informationFall 2010 Graduate Course on Dynamic Learning
Fall 200 Graduae Course on Dynamc Learnng Chaper 4: Parcle Flers Sepember 27, 200 Byoung-Tak Zhang School of Compuer Scence and Engneerng & Cognve Scence and Bran Scence Programs Seoul aonal Unversy hp://b.snu.ac.kr/~bzhang/
More informationV.Abramov - FURTHER ANALYSIS OF CONFIDENCE INTERVALS FOR LARGE CLIENT/SERVER COMPUTER NETWORKS
R&RATA # Vol.) 8, March FURTHER AALYSIS OF COFIDECE ITERVALS FOR LARGE CLIET/SERVER COMPUTER ETWORKS Vyacheslav Abramov School of Mahemacal Scences, Monash Unversy, Buldng 8, Level 4, Clayon Campus, Wellngon
More informationIn the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!") i+1,q - [(!
ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL The frs hng o es n wo-way ANOVA: Is here neracon? "No neracon" means: The man effecs model would f. Ths n urn means: In he neracon plo (wh A on he horzonal
More informationLearning Objectives. Self Organization Map. Hamming Distance(1/5) Introduction. Hamming Distance(3/5) Hamming Distance(2/5) 15/04/2015
/4/ Learnng Objecves Self Organzaon Map Learnng whou Exaples. Inroducon. MAXNET 3. Cluserng 4. Feaure Map. Self-organzng Feaure Map 6. Concluson 38 Inroducon. Learnng whou exaples. Daa are npu o he syse
More informationSingle and Multiple Object Tracking Using a Multi-Feature Joint Sparse Representation
Sngle and Mulple Objec Trackng Usng a Mul-Feaure Jon Sparse Represenaon Wemng Hu, We L, and Xaoqn Zhang (Naonal Laboraory of Paern Recognon, Insue of Auomaon, Chnese Academy of Scences, Bejng 100190) {wmhu,
More informationCHAPTER 5: MULTIVARIATE METHODS
CHAPER 5: MULIVARIAE MEHODS Mulvarae Daa 3 Mulple measuremens (sensors) npus/feaures/arbues: -varae N nsances/observaons/eamples Each row s an eample Each column represens a feaure X a b correspons o he
More informationMANY real-world applications (e.g. production
Barebones Parcle Swarm for Ineger Programmng Problems Mahamed G. H. Omran, Andres Engelbrech and Ayed Salman Absrac The performance of wo recen varans of Parcle Swarm Opmzaon (PSO) when appled o Ineger
More informationVideo-Based Face Recognition Using Adaptive Hidden Markov Models
Vdeo-Based Face Recognon Usng Adapve Hdden Markov Models Xaomng Lu and suhan Chen Elecrcal and Compuer Engneerng, Carnege Mellon Unversy, Psburgh, PA, 523, U.S.A. xaomng@andrew.cmu.edu suhan@cmu.edu Absrac
More informationApproximation Lasso Methods for Language Modeling
Approxmaon Lasso Mehods for Language Modelng Janfeng Gao Mcrosof Research One Mcrosof Way Redmond WA 98052 USA jfgao@mcrosof.com Hsam Suzuk Mcrosof Research One Mcrosof Way Redmond WA 98052 USA hsams@mcrosof.com
More informationCS286.2 Lecture 14: Quantum de Finetti Theorems II
CS286.2 Lecure 14: Quanum de Fne Theorems II Scrbe: Mara Okounkova 1 Saemen of he heorem Recall he las saemen of he quanum de Fne heorem from he prevous lecure. Theorem 1 Quanum de Fne). Le ρ Dens C 2
More informationThe Analysis of the Thickness-predictive Model Based on the SVM Xiu-ming Zhao1,a,Yan Wang2,band Zhimin Bi3,c
h Naonal Conference on Elecrcal, Elecroncs and Compuer Engneerng (NCEECE The Analyss of he Thcknesspredcve Model Based on he SVM Xumng Zhao,a,Yan Wang,band Zhmn B,c School of Conrol Scence and Engneerng,
More informationThis document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.
Ths documen s downloaded from DR-NTU, Nanyang Technologcal Unversy Lbrary, Sngapore. Tle A smplfed verb machng algorhm for word paron n vsual speech processng( Acceped verson ) Auhor(s) Foo, Say We; Yong,
More informationEcon107 Applied Econometrics Topic 5: Specification: Choosing Independent Variables (Studenmund, Chapter 6)
Econ7 Appled Economercs Topc 5: Specfcaon: Choosng Independen Varables (Sudenmund, Chaper 6 Specfcaon errors ha we wll deal wh: wrong ndependen varable; wrong funconal form. Ths lecure deals wh wrong ndependen
More informationVolatility Interpolation
Volaly Inerpolaon Prelmnary Verson March 00 Jesper Andreasen and Bran Huge Danse Mares, Copenhagen wan.daddy@danseban.com brno@danseban.com Elecronc copy avalable a: hp://ssrn.com/absrac=69497 Inro Local
More informationIntroduction ( Week 1-2) Course introduction A brief introduction to molecular biology A brief introduction to sequence comparison Part I: Algorithms
Course organzaon Inroducon Wee -2) Course nroducon A bref nroducon o molecular bology A bref nroducon o sequence comparson Par I: Algorhms for Sequence Analyss Wee 3-8) Chaper -3, Models and heores» Probably
More information( ) () we define the interaction representation by the unitary transformation () = ()
Hgher Order Perurbaon Theory Mchael Fowler 3/7/6 The neracon Represenaon Recall ha n he frs par of hs course sequence, we dscussed he chrödnger and Hesenberg represenaons of quanum mechancs here n he chrödnger
More informationA Novel Object Detection Method Using Gaussian Mixture Codebook Model of RGB-D Information
A Novel Objec Deecon Mehod Usng Gaussan Mxure Codebook Model of RGB-D Informaon Lujang LIU 1, Gaopeng ZHAO *,1, Yumng BO 1 1 School of Auomaon, Nanjng Unversy of Scence and Technology, Nanjng, Jangsu 10094,
More informationWiH Wei He
Sysem Idenfcaon of onlnear Sae-Space Space Baery odels WH We He wehe@calce.umd.edu Advsor: Dr. Chaochao Chen Deparmen of echancal Engneerng Unversy of aryland, College Par 1 Unversy of aryland Bacground
More informationComparison of Differences between Power Means 1
In. Journal of Mah. Analyss, Vol. 7, 203, no., 5-55 Comparson of Dfferences beween Power Means Chang-An Tan, Guanghua Sh and Fe Zuo College of Mahemacs and Informaon Scence Henan Normal Unversy, 453007,
More informationPanel Data Regression Models
Panel Daa Regresson Models Wha s Panel Daa? () Mulple dmensoned Dmensons, e.g., cross-secon and me node-o-node (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy (c) Pongsa Pornchawseskul,
More informationApproximate Analytic Solution of (2+1) - Dimensional Zakharov-Kuznetsov(Zk) Equations Using Homotopy
Arcle Inernaonal Journal of Modern Mahemacal Scences, 4, (): - Inernaonal Journal of Modern Mahemacal Scences Journal homepage: www.modernscenfcpress.com/journals/jmms.aspx ISSN: 66-86X Florda, USA Approxmae
More informationReactive Methods to Solve the Berth AllocationProblem with Stochastic Arrival and Handling Times
Reacve Mehods o Solve he Berh AllocaonProblem wh Sochasc Arrval and Handlng Tmes Nsh Umang* Mchel Berlare* * TRANSP-OR, Ecole Polyechnque Fédérale de Lausanne Frs Workshop on Large Scale Opmzaon November
More informationHEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD
Journal of Appled Mahemacs and Compuaonal Mechancs 3, (), 45-5 HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Sansław Kukla, Urszula Sedlecka Insue of Mahemacs,
More informationDEEP UNFOLDING FOR MULTICHANNEL SOURCE SEPARATION SUPPLEMENTARY MATERIAL
DEEP UNFOLDING FOR MULTICHANNEL SOURCE SEPARATION SUPPLEMENTARY MATERIAL Sco Wsdom, John Hershey 2, Jonahan Le Roux 2, and Shnj Waanabe 2 Deparmen o Elecrcal Engneerng, Unversy o Washngon, Seale, WA, USA
More informationLi An-Ping. Beijing , P.R.China
A New Type of Cpher: DICING_csb L An-Png Bejng 100085, P.R.Chna apl0001@sna.com Absrac: In hs paper, we wll propose a new ype of cpher named DICING_csb, whch s derved from our prevous sream cpher DICING.
More informationAn Effective TCM-KNN Scheme for High-Speed Network Anomaly Detection
Vol. 24, November,, 200 An Effecve TCM-KNN Scheme for Hgh-Speed Nework Anomaly eecon Yang L Chnese Academy of Scences, Bejng Chna, 00080 lyang@sofware.c.ac.cn Absrac. Nework anomaly deecon has been a ho
More informationTSS = SST + SSE An orthogonal partition of the total SS
ANOVA: Topc 4. Orhogonal conrass [ST&D p. 183] H 0 : µ 1 = µ =... = µ H 1 : The mean of a leas one reamen group s dfferen To es hs hypohess, a basc ANOVA allocaes he varaon among reamen means (SST) equally
More informationRobustness of DEWMA versus EWMA Control Charts to Non-Normal Processes
Journal of Modern Appled Sascal Mehods Volume Issue Arcle 8 5--3 Robusness of D versus Conrol Chars o Non- Processes Saad Saeed Alkahan Performance Measuremen Cener of Governmen Agences, Insue of Publc
More informationJanuary Examinations 2012
Page of 5 EC79 January Examnaons No. of Pages: 5 No. of Quesons: 8 Subjec ECONOMICS (POSTGRADUATE) Tle of Paper EC79 QUANTITATIVE METHODS FOR BUSINESS AND FINANCE Tme Allowed Two Hours ( hours) Insrucons
More informationGENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS. Youngwoo Ahn and Kitae Kim
Korean J. Mah. 19 (2011), No. 3, pp. 263 272 GENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS Youngwoo Ahn and Kae Km Absrac. In he paper [1], an explc correspondence beween ceran
More informationF-Tests and Analysis of Variance (ANOVA) in the Simple Linear Regression Model. 1. Introduction
ECOOMICS 35* -- OTE 9 ECO 35* -- OTE 9 F-Tess and Analyss of Varance (AOVA n he Smple Lnear Regresson Model Inroducon The smple lnear regresson model s gven by he followng populaon regresson equaon, or
More informationBoosted LMS-based Piecewise Linear Adaptive Filters
016 4h European Sgnal Processng Conference EUSIPCO) Boosed LMS-based Pecewse Lnear Adapve Flers Darush Kar and Iman Marvan Deparmen of Elecrcal and Elecroncs Engneerng Blken Unversy, Ankara, Turkey {kar,
More informationFTCS Solution to the Heat Equation
FTCS Soluon o he Hea Equaon ME 448/548 Noes Gerald Reckenwald Porland Sae Unversy Deparmen of Mechancal Engneerng gerry@pdxedu ME 448/548: FTCS Soluon o he Hea Equaon Overvew Use he forward fne d erence
More informationP R = P 0. The system is shown on the next figure:
TPG460 Reservor Smulaon 08 page of INTRODUCTION TO RESERVOIR SIMULATION Analycal and numercal soluons of smple one-dmensonal, one-phase flow equaons As an nroducon o reservor smulaon, we wll revew he smples
More informationTight results for Next Fit and Worst Fit with resource augmentation
Tgh resuls for Nex F and Wors F wh resource augmenaon Joan Boyar Leah Epsen Asaf Levn Asrac I s well known ha he wo smple algorhms for he classc n packng prolem, NF and WF oh have an approxmaon rao of
More informationComb Filters. Comb Filters
The smple flers dscussed so far are characered eher by a sngle passband and/or a sngle sopband There are applcaons where flers wh mulple passbands and sopbands are requred Thecomb fler s an example of
More informationPattern Classification (III) & Pattern Verification
Preare by Prof. Hu Jang CSE638 --4 CSE638 3. Seech & Language Processng o.5 Paern Classfcaon III & Paern Verfcaon Prof. Hu Jang Dearmen of Comuer Scence an Engneerng York Unversy Moel Parameer Esmaon Maxmum
More informationNotes on the stability of dynamic systems and the use of Eigen Values.
Noes on he sabl of dnamc ssems and he use of Egen Values. Source: Macro II course noes, Dr. Davd Bessler s Tme Seres course noes, zarads (999) Ineremporal Macroeconomcs chaper 4 & Techncal ppend, and Hamlon
More informationTime-interval analysis of β decay. V. Horvat and J. C. Hardy
Tme-nerval analyss of β decay V. Horva and J. C. Hardy Work on he even analyss of β decay [1] connued and resuled n he developmen of a novel mehod of bea-decay me-nerval analyss ha produces hghly accurae
More informationJ i-1 i. J i i+1. Numerical integration of the diffusion equation (I) Finite difference method. Spatial Discretization. Internal nodes.
umercal negraon of he dffuson equaon (I) Fne dfference mehod. Spaal screaon. Inernal nodes. R L V For hermal conducon le s dscree he spaal doman no small fne spans, =,,: Balance of parcles for an nernal
More informationEEL 6266 Power System Operation and Control. Chapter 5 Unit Commitment
EEL 6266 Power Sysem Operaon and Conrol Chaper 5 Un Commmen Dynamc programmng chef advanage over enumeraon schemes s he reducon n he dmensonaly of he problem n a src prory order scheme, here are only N
More informationDepartment of Economics University of Toronto
Deparmen of Economcs Unversy of Torono ECO408F M.A. Economercs Lecure Noes on Heeroskedascy Heeroskedascy o Ths lecure nvolves lookng a modfcaons we need o make o deal wh he regresson model when some of
More informationUNIVERSITAT AUTÒNOMA DE BARCELONA MARCH 2017 EXAMINATION
INTERNATIONAL TRADE T. J. KEHOE UNIVERSITAT AUTÒNOMA DE BARCELONA MARCH 27 EXAMINATION Please answer wo of he hree quesons. You can consul class noes, workng papers, and arcles whle you are workng on he
More informationCHAPTER 2: Supervised Learning
HATER 2: Supervsed Learnng Learnng a lass from Eamples lass of a famly car redcon: Is car a famly car? Knowledge eracon: Wha do people epec from a famly car? Oupu: osve (+) and negave ( ) eamples Inpu
More informationNormal Random Variable and its discriminant functions
Noral Rando Varable and s dscrnan funcons Oulne Noral Rando Varable Properes Dscrnan funcons Why Noral Rando Varables? Analycally racable Works well when observaon coes for a corruped snle prooype 3 The
More informationM. Y. Adamu Mathematical Sciences Programme, AbubakarTafawaBalewa University, Bauchi, Nigeria
IOSR Journal of Mahemacs (IOSR-JM e-issn: 78-578, p-issn: 9-765X. Volume 0, Issue 4 Ver. IV (Jul-Aug. 04, PP 40-44 Mulple SolonSoluons for a (+-dmensonalhroa-sasuma shallow waer wave equaon UsngPanlevé-Bӓclund
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm H ( q, p, ) = q p L( q, q, ) H p = q H q = p H = L Equvalen o Lagrangan formalsm Smpler, bu
More informationGenetic Algorithm in Parameter Estimation of Nonlinear Dynamic Systems
Genec Algorhm n Parameer Esmaon of Nonlnear Dynamc Sysems E. Paeraks manos@egnaa.ee.auh.gr V. Perds perds@vergna.eng.auh.gr Ah. ehagas kehagas@egnaa.ee.auh.gr hp://skron.conrol.ee.auh.gr/kehagas/ndex.hm
More informationClustering with Gaussian Mixtures
Noe o oher eachers and users of hese sldes. Andrew would be delghed f you found hs source maeral useful n gvng your own lecures. Feel free o use hese sldes verbam, or o modfy hem o f your own needs. PowerPon
More informationConstrained-Storage Variable-Branch Neural Tree for. Classification
Consraned-Sorage Varable-Branch Neural Tree for Classfcaon Shueng-Ben Yang Deparmen of Dgal Conen of Applcaon and Managemen Wenzao Ursulne Unversy of Languages 900 Mnsu s oad Kaohsng 807, Tawan. Tel :
More informationThe preemptive resource-constrained project scheduling problem subject to due dates and preemption penalties: An integer programming approach
Journal of Indusral Engneerng 1 (008) 35-39 The preempve resource-consraned projec schedulng problem subjec o due daes and preempon penales An neger programmng approach B. Afshar Nadjaf Deparmen of Indusral
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm Hqp (,,) = qp Lqq (,,) H p = q H q = p H L = Equvalen o Lagrangan formalsm Smpler, bu wce as
More informationPredicting and Preventing Emerging Outbreaks of Crime
Predcng and Prevenng Emergng Oubreaks of Crme Danel B. Nell Even and Paern Deecon Laboraory H.J. Henz III College, Carnege Mellon Unversy nell@cs.cmu.edu Jon work wh Seh Flaxman, Amru Nagasunder, Wl Gorr
More informationAppendix H: Rarefaction and extrapolation of Hill numbers for incidence data
Anne Chao Ncholas J Goell C seh lzabeh L ander K Ma Rober K Colwell and Aaron M llson 03 Rarefacon and erapolaon wh ll numbers: a framewor for samplng and esmaon n speces dversy sudes cology Monographs
More informationA NOVEL NETWORK METHOD DESIGNING MULTIRATE FILTER BANKS AND WAVELETS
A NOVEL NEWORK MEHOD DESIGNING MULIRAE FILER BANKS AND WAVELES Yng an Deparmen of Elecronc Engneerng and Informaon Scence Unversy of Scence and echnology of Chna Hefe 37, P. R. Chna E-mal: yan@usc.edu.cn
More informationAuthor s Accepted Manuscript
Auhor s Acceped anuscrp Dscrmnave srucure selecon mehod of gaussan mxure models wh s applcaon o handwren dg recognon Xuefeng Chen Xab Lu Yunde Ja PII: S095-3(0)0047-6 DOI: do:0.06/j.neucom.00..00 Reference:
More informationRelative controllability of nonlinear systems with delays in control
Relave conrollably o nonlnear sysems wh delays n conrol Jerzy Klamka Insue o Conrol Engneerng, Slesan Techncal Unversy, 44- Glwce, Poland. phone/ax : 48 32 37227, {jklamka}@a.polsl.glwce.pl Keywor: Conrollably.
More informationJoint Channel Estimation and Resource Allocation for MIMO Systems Part I: Single-User Analysis
624 IEEE RANSACIONS ON WIRELESS COUNICAIONS, VOL. 9, NO. 2, FEBRUARY 200 Jon Channel Esmaon and Resource Allocaon for IO Sysems Par I: Sngle-User Analyss Alkan Soysal, ember, IEEE, and Sennur Ulukus, ember,
More informationBayesian Inference of the GARCH model with Rational Errors
0 Inernaonal Conference on Economcs, Busness and Markeng Managemen IPEDR vol.9 (0) (0) IACSIT Press, Sngapore Bayesan Inference of he GARCH model wh Raonal Errors Tesuya Takash + and Tng Tng Chen Hroshma
More informationUsing Fuzzy Pattern Recognition to Detect Unknown Malicious Executables Code
Usng Fuzzy Paern Recognon o Deec Unknown Malcous Execuables Code Boyun Zhang,, Janpng Yn, and Jngbo Hao School of Compuer Scence, Naonal Unversy of Defense Technology, Changsha 40073, Chna hnxzby@yahoo.com.cn
More informationSOME NOISELESS CODING THEOREMS OF INACCURACY MEASURE OF ORDER α AND TYPE β
SARAJEVO JOURNAL OF MATHEMATICS Vol.3 (15) (2007), 137 143 SOME NOISELESS CODING THEOREMS OF INACCURACY MEASURE OF ORDER α AND TYPE β M. A. K. BAIG AND RAYEES AHMAD DAR Absrac. In hs paper, we propose
More informationImproved Classification Based on Predictive Association Rules
Proceedngs of he 009 IEEE Inernaonal Conference on Sysems, Man, and Cybernecs San Anono, TX, USA - Ocober 009 Improved Classfcaon Based on Predcve Assocaon Rules Zhxn Hao, Xuan Wang, Ln Yao, Yaoyun Zhang
More informationBernoulli process with 282 ky periodicity is detected in the R-N reversals of the earth s magnetic field
Submed o: Suden Essay Awards n Magnecs Bernoull process wh 8 ky perodcy s deeced n he R-N reversals of he earh s magnec feld Jozsef Gara Deparmen of Earh Scences Florda Inernaonal Unversy Unversy Park,
More informationFast Space varying Convolution, Fast Matrix Vector Multiplication,
Fas Space varyng Convoluon Fas Marx Vecor Mulplcaon l and FMRI Acvaon Deecon Janng We Advsors: Prof. Jan P. Allebach Prof. Ilya Pollak Prof. Charles A. Bouman Dr. Peer A. Jansson School of Elecrcal and
More information. The geometric multiplicity is dim[ker( λi. A )], i.e. the number of linearly independent eigenvectors associated with this eigenvalue.
Mah E-b Lecure #0 Noes We connue wh he dscusson of egenvalues, egenvecors, and dagonalzably of marces We wan o know, n parcular wha condons wll assure ha a marx can be dagonalzed and wha he obsrucons are
More information